When the artist Hieronymus Bosch passed away 500 years ago in the little Dutch town of ’s-Hertogenbosch, he left behind an astonishing and groundbreaking portfolio — with intricate scenes of monstrous figures doing the wackiest things — that continue to inspire disciples and perplex experts to this day.

Madrid’s Prado Museum, longtime home to several of Bosch’s most famous works, including his masterpiece, “The Garden of Earthly Delights,” is paying deep respect to the artist this summer with “Bosch: The 5th Centenary Exhibition,” the first time that so many of his works have been shown together at once, and most likely the last time they ever will again.

Madrid’s steeple-filled skyline.Jose Barea/Madrid Destino

With 21 original paintings and eight original drawings (plus many pieces from painters of his school and other artists of his day), the Prado show includes more than three-quarters of Bosch’s surviving catalog.

That’s more than even his own hometown museum, the Noordbrabants, was able to muster with its own quincentennial exhibition earlier this year.

So just how is it that the Spanish capital became home to so much of the work of this early Dutch master? Thank Philip II, Spain’s art-loving 16th-century king, who snatched up as many Bosches as he could for his private collection — which eventually, along with the rest of the massive Spanish royal art hoard, provided the basis for the Prado Museum when it opened in 1819.

With a dizzying permanent collection of more than 20,000 pieces including Diego Velázquez’s “Las Meninas” and numerous famed works by El Greco, Titian, Rubens and Goya, the Prado is now one of Madrid’s top tourist attractions, and the grand dame of the city’s so-called golden triangle of art that straddles the tree-lined boulevard of Paseo del Prado.

Attendance at the once-in-a-lifetime Bosch show (which runs through Sept. 11) has been heavy, as international crowds angle to get close to mesmerizing works by the artist whose wildly over-the-top creatures earned him the contemporary nickname ”the devil maker.” His downright frightening style has even caused historians to speculate that he may have been under the influence of psychedelic drugs. (Most agree that he probably wasn’t, but merely used his extremely vivid imagination to warn his fellow late medieval Christians of the beastly dangers of sin.)

Bosch’s large and beautifully restored triptych, “The Garden of Earthly Delights,” with its elaborate and brightly colorful visions of paradise, earth and hell, is the star of the show — and it’s also inspired a tandem installation called “Infinite Garden,” an immersive multimedia experience that’s newly opened at the Prado since July 4 (museum admission 16 euro during Bosch exhibition).

(Before you go: Brush up on your Bosch with the new Dutch documentary “Hieronymus Bosch: Touched by the Devil,” which screens at New York City’s Film Forum in its premiere US engagement from July 27 to Aug. 9.)

Spectators spectating a piece at Thyssen-Bornemisza.Adrian Tyler

Just across from the Prado, on the other side of the Neptune-fountained Plaza de Canovas del Castillo, lies one of the world’s most esteemed private art museums, the Thyssen-Bornemisza. The broad collection — spawned in the 1920s by a German-Hungarian baron who wisely bought as much art as he could from cash-poor Depression-era American millionaires — made its way to Madrid after the baron’s son took a former Miss Spain as his fifth wife.

The Thyssen-Bornemisza opened in 1992 with much of the family’s collection, and now displays about 1,000 paintings spanning eight centuries and scores of art movements, from early European Renaissance on through to American Pop (museum admission 12 euro). Thanks to its international clout, the museum is also able to host excellent temporary exhibitions, like the current “Caravaggio and the Painters of the North” (through Sept. 21) and the upcoming 70-work “Renoir and Intimacy” (opening Oct. 18).

The generously glassed Reina Sofia Museum. Joaquin Cortes/Roman Lores

A pretty 15-minute stroll south along Paseo del Prado — including an obligatory quick stop to admire the striking 15,000-plant vertical garden hugging the side of the CaixaForum Madrid cultural center — leads to the third point in the triangle: the Reina Sofía Museum.

Also opened in 1992, the Reina Sofía is the world’s foremost keeper of 20th-century Spanish art, all housed on a sprawling site made up of what was once Madrid’s General Hospital, plus a contemporary red 86,000-square-foot extension by French architect Jean Nouvel that was added in 2005.

With superb collections of works by Pablo Picasso and Salvador Dalí (including Picasso’s huge “Guernica,” the museum’s most famous piece), the Reina Sofía is the world’s 13th most visited art museum, far ahead of the busy Prado at number 19, and besting even New York’s MoMA at number 14 (8 euro permanent collection, four euro temporary exhibitions. A ”Paseo del Arte” ticket grants admission to all three museums for 28.80 euro).

The Reina Sofía’s vast size makes the crowds feel smaller, and also allows it to host multiple temporary exhibitions simultaneously, with six right now including a retrospective of Cuban painter Wilfredo Lam (through Aug. 15) and “Campo Cerrado,” a survey of Spanish art from 1939 to 1953 (through Sept. 26).